A can do a piece of work in 10 days and B can do it in 12 days. They work together for 2 days, then B leaves and A alone continues. 3 days later C joins and the work is completed in 2 more days. In how many days can C do the work alone?

15 days  

Work done by A and B together in 2 days = efficiency x no. of days = 11 x 2 = 22

Work left after this = 60 - 22 = 38

This work is continues by A alone in the next 3 days,

With efficiency of 6, work done by A = 6 x 3 = 18 

Work lefty thereafter, 38 - 18 = 20

This is completed by A and C in 2 days, 

then efficiency of A and C together = \(\frac{work}{no.\; of\;\; days}\) 

                                                   =\(\frac{20}{2}\) = 10

Efficiency of C = 10 - 6 = 4

Time taken C alone to do the total work = \(\frac{Total\; work }{efficiency}\)

                                                          = \(\frac{60}{4}\) = 15 days